Statistical Inference for Lindley Model based on Type II Censored Data

Abstract

In this paper, the moment-based, maximum likelihood and Bayes estimators for the unknown parameter of the Lindley model based on Type II censored data are discussed. The expectation maximization (EM) algorithm and direct maximization methods are used to obtained the maximum likelihood estimator (MLE). Existence and uniqueness of the moment-based and maximum likelihood estimators are discussed and a bias corrected estimator based on parametric bootstrap is developed. For Bayesian estimation, since the Bayes estimator cannot be obtained in an explicit form, two approximations based on Lindley and the importance sampling methods are used. Asymptotic confidence intervals, bootstrap confidence intervals and credible intervals are also proposed. Based on Type II censored data, the prediction of future observations is discussed. The analysis of a real data has been presented for illustrative purposes. Finally, Monte Carlo simulations are performed to compare the performances of the proposed estimation methods.

On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions

“…Bhati, Sastry, and Maha-Qadri (2015) have proposed a generalized Poisson-Lindley distribution and studied its applications and properties in detail. Asgharzadeh, Ng, Valiollahi, and Azizpour (2017) have discussed inferential procedures for the Lindley distribution based on type II censoring scheme. Asgharzadeh, Fallah, Raqab, and Valiollahi (2018) have provided statistical inference for the Lindley distribution based on record data.…”

Statistical Inference for Two Gumbel Type-II Distributions under Joint Type-II Censoring Scheme

“…Thus, it can be seen that ξ 1 (α 1 ), ξ 2 (α 2 ) and ξ 3 (β) are the continuous functions on (0, +∞), which decrease monotonically from +∞ to negative quantity (U).Therefore, the MLEs of α j and β, j = 1, 2 exist and are the solution of ξ 1 (α 1 ) = 0, ξ 2 (α 2 ) = 0, and ξ 3 (β) = 0 and they are unique if m r < m < 2m r and n r < n < 2n r (see [23]).…”